# Minor Loss in Pipe or Duct Components

## Minor loss, pressure or head loss in pipe, tube and duct system components

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Pressure loss in straight pipes or ducts are called **major loss** (linear loss). Pressure loss in components like valves, bends, tees and similar are called **minor loss** (local loss)

Minor loss can be significant compared to major loss. In fact - when a valve is closed or nearly closed - the minor loss is infinite. For an open valve the minor loss can often be neglected (typical for a full bore ball valve).

### Minor Loss

Pressure drop or the minor loss in components correlates with the dynamic pressure in the flow and can be expressed as

p_{minor_loss}= ξ (1/2) ρ v^{2}(1)

or

h_{minor_loss}= ξ v^{2}/ (2 g)(2)

where

p_{}_{minor_loss}= minor pressure loss (Pa (N/m^{2}), psf (lb/ft^{2}))

ρ= density (kg/m^{3}, slugs/ft^{3})

v= flow velocity (m/s, ft/s)

h_{minor_loss}= minor head loss (m, ft)

g= acceleration of gravity (9.81 m/s^{2},32.174 ft/s)^{2 }

*1 psf = 0.00694 psi**(lb/in*^{2})

The minor loss coefficient - *ξ* - values ranges from *0 * and upwards. For *ξ** = 0* the minor loss is zero and for *ξ =** 1* the minor loss is equal to the dynamic pressure or head. The minor loss coefficient can also be greater than 1 for some components.

### Minor Loss Coefficient

The **minor loss coefficient** can be expressed as:

ξ = p_{minor_loss}/ ((1/2) ρ v^{2})(3)

or

ξ = h_{minor_loss}/ (v^{2}/ (2 g))(4)

The minor loss in components depends primarily on the geometrical construction of the component and the impact the construction has on the fluid flow due to change in velocity and cross flow fluid accelerations.

The fluid properties - in general expressed with the Reynolds number - also impacts the minor loss.

The head loss information about components is given in dimensionless form and the information is based on experiments.

- Minor Loss Coefficients for Piping and Tube Components
- Minor Loss Coefficients for Air Duct Components

### Equivalent Length

The minor loss in a system component can be converted to a length equivalent to a pipe or tube that would give the same major head loss.

Major head loss can be expressed as:

*h _{major_loss} = λ (l / d_{h}) (v^{2}/ (2 g)) *

*(5)*

*where*

*h _{major_loss} =* major head loss (m, ft)

*λ** = friction coefficient*

*l** = length of pipe or duct (m, ft)*

*d _{h}*

*= hydraulic diameter related to the pipe or tube with the component (m, ft)*

If we want the minor loss to be equal to the major loss for a given equivalent length of pipe or duct - then

*h _{minor_loss} = h_{major_loss_eq (6)}*

*or *

* ξ v ^{2}/ (2 g) = λ (l_{eq} / d_{h}) (v^{2}/ (2 g)) (6b)*

*where *

*h _{major_loss_eq }*= equivalent major head loss (m, ft)

*l _{eq}*

*= equivalent length of pipe or duct (m, ft)*

Equivalent length can then be expressed by transforming *(6b)* to:

*l _{eq} = ξ d_{h} / λ*

*(7)*

The Total Head Loss of the pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems - plus the sum of the equivalent lengths of all the components in the system.

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